A stale remote service is a service for which AppDynamics has previously captured metrics, but which has experienced no metric activity for a certain time period. If a backend is not called for 30 days (in other words, the call per minute metric is zero for 30 days) AppDynamics considers it a stale backend and removes it as a monitored artifact.
After a backend is removed, its metrics no longer appear in the Metric Browser and health rules that reference those metrics do not fire. You should remove any health rules conditions that reference metrics in stale backends.
For an on-premises Controller, you can configure the interval by setting the backend.permanent.deletion.period property in the Administration Console. Reducing the period may be advisable for large installations, since the maximum number of backends removed in one pass is 50. The minimum interval is one week. Alternatively, you can disable automatic removal by setting the interval to 0.